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本文推广捷克学者柯鲁塞克(C.V.Kloucek)的形变分配法,把结点位移为一个未知量的情况推广到二个未知是的情况。采用二阶矩阵(文中称为小矩阵)来表示结点位移及传递系数等一切有关的量,进行推导整理,得到与形变分配法完全相同的公式形式。不过公式中符号不再是一个数而是一个二阶列阵或方阵,因此称为形变矩阵分配法。文中用此法求出多跨连续拱承受结点荷载的精确解;对于承受一般荷载情况,则再结合《拱桥设计计算手册》就可完全解决。文中还较仔细地考虑了拱座偏心、桥台移动、墩柱沉陷及温度影响的算法。公式形式规则整齐,计算简单易行,用普通计算器就可以完成全部计算。文中以某桥为实例作了计算,作出了拱顶弯矩和桥墩水平力影响线。《影响线的规律以及和单跨无铰拱影响线的比较可看出本文的算法是正确的。
This article promotes the deformation distribution method of the Czech scholar C.V. Kloucek, and extends the situation where the node is displaced to an unknown quantity to the case of two unknowns. A second-order matrix (referred to as a small matrix in the text) is used to represent all the relevant quantities such as the node displacement and the transfer coefficient, and the derivation is carried out to obtain the exact same formula as the deformation distribution method. However, the symbol in the formula is no longer a number but a second-order array or square matrix, so it is called the deformation matrix allocation method. In this paper, the exact solution of the multi-span continuous arch subjected to the joint load is obtained by this method. For the general load situation, it can be completely solved by combining the “Architecture Design Calculation Manual”. The algorithm of the eccentricity of the abutment, the movement of the abutment, the subsidence of the pier and the influence of the temperature was also considered in detail. The rules of formulae are neat, the calculation is simple and easy, and all calculations can be completed with an ordinary calculator. In this paper, a bridge is taken as an example for calculation, and the influence lines of the bending moment of the dome and the horizontal force of the pier are made. "The rule of the influence line and the comparison with the single-span unhinged arch influence line can be seen that the algorithm of this paper is correct.